Moment Lyapunov exponents and stochastic nonstability of a circular cylindrical shells

Abstract

The paper investigates the stochastic stability conditions of circular cylindrical shells, compressed by time-dependent stochastic membrane forces. The main contribution of the paper is the determination of the moment Lyapunov exponents of the linear cylindrical shell for the first time. The moment and almost-sure stochastic stability of a three-degree-of-freedom coupled continuous system, under parametric excitation of white noise, are investigated. It is assumed that the system possesses a small damping. This type of a shell structure model requires a specific scheme for determining the moment Lyapunov exponents. The system of stochastic differential equations of motion is decoupled by using the contact transformation method with the obtained appropriate symplectic matrix of the system. Then a scheme for determining the moment Lyapunov exponents is presented which contains an analytical procedure. The largest Lyapunov exponent is calculated through its relation with the moment Lyapunov exponent. The moment and almost-sure stability boundaries are obtained analytically. These results are important and useful in engineering applications as an example of a procedure for dynamic analysis of mechanical systems with coupled stochastic oscillators.